Fingerprint template generation, verification and identification system

ABSTRACT

A system to generate a template of a fingerprint input image is described. The system provides for smoothing the input image, forming a binary image from it, and further processing the binary image to extract the minutia of the fingerprint. The minutiae are stored in the template, in the form of locations of each minutia in relation to all other minutiae. The system includes optional identification and verification steps, which compare the template generated according to the system with templates stored in a fingerprint database.

FIELD OF THE INVENTION

The present invention relates to methods and systems of identificationusing fingerprint biometrics.

BACKGROUND OF THE INVENTION

Since the early days of society there has been a significant need topositively identify persons, to grant or deny them access to places,information, property etc. With the advent of modern technologies, theability of even a single person to collect information, cause damage oraffect events has increased exponentially, making it more important thanever to positively ensure that someone really is who he or she claims tobe. Additionally, it is also important to identify unknown persons, forexample to determine whether they may be of interest to security or lawenforcement organizations.

The importance and value of identification systems cannot be overstate.In addition to addressing the better known national security issues suchas espionage, sabotage etc, more recent concerns over terrorism andindustrial espionage have demanded fast and accurate methods ofidentification, which cannot easily be defeated by a determinedopponent. These methods are useful not only to secure access to physicallocations, such as military, governmental and industrial sites, but alsoto limit access to information stored in electronic devices such ascomputers, which may be connected to worldwide networks.

Identification cards and access codes have been used to identify personsand to grant access, but they have severe limitations. Cards can belost, stolen or forged, and codes/passwords can be forgotten or obtainedby the wrong persons. Biometrics provides a solution to these issues.Biometrics is the statistical observation and measurement of biologicalphenomena, such as the characteristics that differentiate one personfrom another. These biometric characteristics are used to identify andvalidate someone's identity. Perhaps the oldest form of biometricidentification involves comparing fingerprints of a person to knownfingerprints. This method can be very accurate, but is often timeconsuming if done manually, and resource intensive if carried out bymachine. In addition, imperfect fingerprints due to contamination orinjury of the fingers or to a partial fingerprint make the comparisonproblem even more difficult.

SUMMARY OF THE INVENTION

In one aspect, embodiments of the present invention include a method forfingerprint recognition, which includes providing a machine readableinput fingerprint image, smoothing the input fingerprint image to removenoise, binarizing the smoothed input fingerprint image to form a binaryimage, processing the binary image to identify minutiae of thefingerprint image, and generating a template describing the minutiae.

In a different aspect, the present invention is a system for analyzingfingerprints. The system includes a software module configured toreceive an input fingerprint image, the input fingerprint image havingdark portions representing fingerprint ridges and light portionsrepresenting fingerprint furrows, the software module further configuredto generate a binary image from the input fingerprint image, and toextract a set of minutiae from the binary image. The system alsoincludes a memory module configured to store a template of locationinformation of the set of minutiae.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a drawing showing a typical input fingerprint image usedaccording to embodiments of the present invention;

FIG. 2 is a schematic diagram showing the input fingerprint image ofFIG. 1 after binarizing and thinning operations, according to anembodiment of the present invention;

FIG. 3 is a schematic drawing of a grid encompassing neighboring pixelsused to determine the location of minutiae according to an embodiment ofthe invention;

FIGS. 4 a and 4 b are schematic diagrams showing the minutiae derivedfrom the fingerprint of FIG. 1, according to different embodiments ofthe present invention;

FIG. 5 is a flowchart describing the template generation and comparisonmethod according to an embodiment of the present invention; and

FIGS. 6 a, 6 b and 6 c are diagrams showing a mask superimposed onfingerprint features, according to another embodiment of the invention.

DETAILED DESCRIPTION

The present invention may be further understood with reference to thefollowing description and the appended drawings, wherein like elementsare referred to with the same reference numerals. Biometric techniquesmay be used to identify persons by comparing their biometriccharacteristics to a database of biometric characteristics of knownindividuals, and finding a matching entry. The same techniques may beused to verify a person's identity, by comparing their biometriccharacteristics to those of the person they purport to be. Fingerprintbased biometric identification is one of the oldest methods which hasbeen used successfully in various applications. It is well known thatevery person has unique, immutable fingerprints, which may be used todistinguish them from other persons. Fingerprints may be comparedvisually by trained personnel, but for large scale and rapid operationsthe use of machine comparison is necessary.

Fingerprints are made of a series of ridges and furrows or valleysformed on the surface of the finger's skin. Each fingerprint is unique,as determined by the pattern of ridges and furrows, which form theelevated and depressed portions of the fingertips, respectively. Inparticular, the intersections of multiple ridges are of interest, andare called the minutiae of the fingerprint. Minutiae points arecharacteristics of the pattern of ridges, which identify a ridgebifurcation or a ridge ending. The pattern of minutiae may also be usedto identify the fingerprint. Although this method does not take intoaccount the global shape of the ridges and the furrows of thefingerprint, it is generally considered sufficiently accurate toidentify the person to whom the fingerprint belongs. Comparing minutiaerather than the entire fingerprint makes the process faster and lessresource intensive.

Before analyzing the minutiae, it should be determined whether to followthe pattern of ridges or of furrows of the fingerprint. Both willgenerally follow the same outline, but for simplicity either the ridgesor the furrows should be mapped, and not both. In the present example,ridges may be followed to determine the location of minutiae. FIG. 1shows a typical fingerprint 10, as would be obtained from a conventionalinked fingerprint card, or from an electronic scanner. In thisrepresentation, the ridges appear as dark lines 14, and the furrows aslight lines 12. This mimics the results obtained using inked fingerprintcards, where the finger is coated with ink, and is pressed against thecard. The raised ridges deposit ink on the card, while the furrows donot. In the case of an electronic scanner, for example one using chargecoupled devices to detect light, different representations may beselected, without affecting the validity of the present invention. Thescanner's electronic sensors detect the different reflectivity of ridgesand furrows, and may assign a different color to each, for example blackand white.

If the input fingerprint image that is to be analyzed is an analogdrawing or representation, the first step that should be carried out isto convert the image to a format that is machine readable. For example,the image may be digitized with a conventional scanner, such that eachpixel of the image is described in terms of a numerical code. This stepmay be carried out in any conventional manner which results in a digitalgraphic file that may be read and used, for example, by an electronicprocessor. This step will generally be necessary if the inputfingerprint image is formed by ink on paper, such as the well knownfingerprint cards.

Once the fingerprint image is in a condition that can be manipulated bymachine, for example after the digital image has been generated, asmoothing operation may be carried out. This operation remove noise fromthe input image signal, so that a more accurate and efficient processingcan take place subsequently. It is important that the image be devoid ofnoise as much as practical, to minimize errors in determining theminutiae of the fingerprint. Noise may be due, for example, to dirt orinjuries to the fingers when the fingerprint is taken, or simply to poorquality of the fingerprint input image. For example, algorithms may beused to evaluate the shapes present in the input fingerprint image, andeliminate pixels that do not conform to known fingerprint patterns.Those of skill in the art will understand that other conventional imagesmoothing processes may be utilized for this purpose, while remainingwithin the scope of the present invention.

After the initial smoothing operation is carried out, a binarizationstep may take place. This operation involves representing thefingerprint as a binary image, consisting of an array of 0 and 1 digits.For example, every pixel of the fingerprint image that depicts a blackpoint, corresponding to a ridge, may be represented by a digit 1.Conversely, every white pixel corresponding to a furrow may berepresented by a digit 0. This representation is necessary to allow anelectronic process to manipulate the image, and eventually extract theminutiae 20 such as ridge termination 16 and ridge bifurcation 18 shownin FIG. 1. In some cases, the input fingerprint image 10 may containpixels that are of a color that is not clearly black or white, butrather of a tone of gray. This eventuality may be resolved by specifyinga threshold value or value range of the pixels, below which a pixelvalue of 0 is assigned, and above which a pixel value of 1 is assigned.The threshold value may be a level of gray of the pixel, or a level ofwhichever property is used to distinguish between furrows and ridges.

The binary image at this point contains lines that correspond, forexample, to the fingerprint ridges 14 shown in FIG. 1. However, theselines may have different thicknesses, due to different thicknesses ofthe ridges on the person's finger, or simply to distortion occurringwhen obtaining and manipulating the input fingerprint image 10. Athinning operation may be carried out to remedy this problem, sincelines of uneven thickness make the determination of minutiae moredifficult. Thinning consists of normalizing all the lines describing theridges and furrows of the fingerprint, so that every line has a width ofone pixel. In other words, lines that start with a thickness of morethan one pixel, or that have sections with a varying width, afterthinning will have a uniform width of one pixel. Conventional algorithmsmay be used to perform this function. For example, the centerline ofeach line may be numerically computed, and the line may be re-drawnalong that centerline, with the desired width of one pixel.

FIG. 2 shows the result of thinning on the image of FIG. 1. The samepattern of ridges and furrows is retained in thinned image 30 as it wasin the input fingerprint image 10 of FIG. 1, but now lines 32representing the are all of the same width, in this case one pixel.Minutiae 36 are the same as before the operation, for example with ridgeend 38 and ridge bifurcation 34 remaining in the same location. Thethinning or normalization process thus results in a thinned fingerprintimage 30 where every line has the same one pixel width along its entirelength. All the characteristics of the input fingerprint image areretained, including the location and number of minutiae, and the globalshape of the ridges and furrows. As will be described below, thinningthe image considerably simplifies the process of isolating minutiae fromthe image.

As indicated above, minutiae may be defined by the ends and thebifurcations of lines representing the ridges of the fingerprint.Accordingly, one way to determine the location of a minutia is to lookfor points that are not within a single line segment, but rather are atthe end of a segment or at the intersection of multiple segments. Pointsthat are part of a single line will have only one line segment behindthem and only one line segment in front. Termination points 16 will haveonly one segment behind them, with no segments in front. Bifurcationpoints 18 will have more than two line segments ahead and/or behindthem, as shown in FIG. 1. To simplify the recognition of minutiae, thescheme may be simplified by only considering bifurcation minutiae torepresent the fingerprint. This simplification may reduce somewhat theaccuracy of the fingerprint representation, but not enough to reducesignificantly the validity of the method. In return, the simplerrepresentation may be much faster and more efficient than using allminutiae in representing the fingerprint.

Since the thickness of the ridge lines has been normalized to equal onepixel in the thinning process, a simple method may be used to determinethe location of bifurcation minutiae. Every pixel representing a pointalong the length of a ridge line of the thinned fingerprint image isanalyzed. As shown in FIG. 3, a grid 50 is constructed around the pixel,which is centered at cell 52 of grid 50. Each cell is approximately thesize of a pixel, and thus may only contain one pixel. In this example, apixel 54 of thinned line 32 is centered at cell 52. (The actual width ofline 32 is not shown in the drawing.) The cells of grid 50 are numbered0–8, and each corresponds to pixel 54 and to one of the eightneighboring pixels of pixel 54. As we move from one cell to the next,every time that a change from 0 to 1 is seen in the pixel value of thepixels, the value of a transition sum summation counter is increased byone, starting from a zero value. This is done to determine whether pixel54 represents a bifurcation, thus a minutia. The pixel values of eachpixel have been set in the binarization step, as described above, andare 0 for white pixels that do not represent points on the fingerprintridge lines, and 1 for black pixels that represent points on the ridgelines.

Since each cell 0–7 contains one pixel only with a pixel value of 1 or0, the transition sum computed by noting changes of the neighboringpixel values indicates the type of point found in cell 52. If thetransition sum is equal to at least 3, it means that at least threeneighboring points of pixel 54 have a value of 1, indicating that abifurcation exists at point 54. A termination may be indicated when thetransition sum equals to one. Generation of the transition sum may bereferred to as the Zero-One Sequence count, in reference to the pixelvalues being observed. In case the fingerprint ridge line divides intomore than two branches, the transition sum will have a correspondinglyhigher value. In this exemplary embodiment, the transition sumindicating the number of transitions from 0 to 1 pixel value is carriedout by moving through the cells in the order of cells 1, 2, 3, 4, 5, 6,7 and 0. However, the same result may be reached by moving through thecells in a different order. In the example shown in FIG. 3, pixel 54corresponds to a bifurcation point 36, and the corresponding transitionsum equals to at least three, such that the presence of a minutia wouldbe noted at cell 52. The existence of a minutia may thus be determinedby computing the transition sum for all pixels depicting fingerprintfeatures, and comparing each transition sum to a selected value (forexample three) that acts as a threshold.

Other methods for computing the location of minutiae may be usedaccording to embodiments of the invention. For example, a masking andY-sequence method may be utilized, as shown in FIGS. 6 a, 6 b and 6 c.According to this method, a first step comprises superimposing a mask 58of M by N dimensions over successive segments of the fingerprintfeatures. In this example, the features may be ridges to which have beenassigned black pixels. An x-y coordinate system with origin (0,0) at thebottom left corner of the mask 58 is also included. Within the mask,moving on a path along the x-axis from (0,0) to (M−1,0), vertical linesare extended from points on the path to a height on the y-axis of N−1.These may be drawn at M equidistant points. For example, at a locationx=i, the vertical line would extend from (i, 0) to (i, N−1). Along eachof the vertical lines a Y_(avg) value is computed according to theformula:

$Y_{avg} = {( {\overset{- 1}{\sum\limits_{i = 0}}Y_{i}} )/N}$In the formula, only the Y, values corresponding to a black pixel aresummed, over the length of the vertical line from y=0 to y=N−1. Sinceeach mask 58 has M vertical lines, the process generates M values ofY_(avg) listed in sequential order, which are referred to as the Yssequence.

The pattern of numbers in the Ys sequence may be used to determine if abifurcation, thus a minutia, is present along the segment within themask. In essence, the Y_(avg) elements of the Ys sequence represent theaverage value of the y coordinate of all black pixels along a verticalline. In the example of FIG. 6 a, a single line without bifurcations 60exists in the mask region, and the Ys elements will be in increasingorder if the segment is curved up, and in decreasing order if thesegment is curved down. Since only one line segment exists at thosepoints, all the Y_(avg) values will map to black areas, as shown by line70. If a genuine bifurcation point exists within the mask, as shown inFIG. 6 b, the Y_(avg) values will be either in decreasing or increasingorder, but will map to a white area for points along the x-axis wheremore than one line segment 62, 64 exists (i.e on line 72), and will mapto black areas where only one segment 62 exists (i.e. on line 74). Inthe case shown in FIG. 6 c two parallel lines 66, 68 exist within mask58. Here, all the Y_(avg) values map in the white areas (on lines 76,78), since the average y-coordinate of the black pixels never falls oneither line segment.

The masking and Y-sequence method thus offers an exemplary alternativeto determining the location of minutiae. This method may be carried outwith or without a prior thinning step, since the averaging proceduredoes not require line segments that are one pixel wide, but can processsegments of varying width. Although vertical lines were used in thisexample, lines in other orientations may also be used according to thismethod. The dimensions of the mask is important, and should be selectedconsidering the size of the fingerprint features to be analyzed. Thespecific method used to isolate the minutiae may be selected dependingon the application, based on required speed, accuracy and on theavailable computing resources. Those of skill in the art will understandthat additional variations of these methods may be employed, withoutexceeding the scope of the present invention.

After evaluating all the pixels corresponding to fingerprint ridge linesin thinned fingerprint image 30, all the minutia representingbifurcation points can be mapped. FIG. 4 a shows an example of suchmapping 40, where fingerprint ridge lines 32 have been removed, and onlyminutiae 36 are shown. In this exemplary embodiment, only minutiaecorresponding to bifurcations 34 are shown. FIG. 4 b shows a differentembodiment according to the invention, in which minutiae 36 correspondto both bifurcations 34 and terminations 38. At this point a fingerprinttemplate may be constructed, which essentially provides a short handdescription of the entire fingerprint which can be rapidly manipulated,for example, by an electronic processor. In one exemplary embodimentaccording to the present invention, the template may be constructed bydescribing, for each minutia point, position information of that minutiapoint. In one example, the position information of the template mayinclude the distance of every minutia point from all other minutiaepoints.

In addition to the position information, gradient information may alsobe included in the template, to further create a unique representationof the fingerprint. The gradient information is not necessary to definea template, but may be useful in certain applications. Gradientinformation gives the slope of the line segments extending from theminutia being described, thus indicating if those segments extendupward, downward or horizontally from the minutia. In the case of aminutia defined by a branching, there will be at least three slopevalues describing the three segments extending from the branching. Thetemplate may be stored in a database for further manipulation, asdescribed below, and its specific format may be tailored to the type ofmatching to be performed with it. In one example, the template may be atwo-dimensional matrix with rows representing different minutiae, andcolumns within a row representing the distance from that minutia to eachof the other minutiae. The distances from other minutiae may be listedin ascending order.

The template generated as described above may be used for two principalpurposes. In one case, the template of an individual claiming to be acertain person may be used to validate the identity of that individual.In this process, a fingerprint of the individual is analyzed to generatea corresponding template. The template is then compared to a previouslystored template generated from the person the individual claims to be.If the templates match, the individual is likely the person he claims tobe, otherwise further investigation is necessary. In a second case, thetemplate of an unknown individual may be used for identification of theindividual. In this case, the template generated from the individual'sfingerprints is compared to all the templates stored, for example, in adatabase of fingerprints belonging to known persons. When a match isfound, the unknown individual is identified.

In many cases, the match between the template generated from thefingerprints to be verified or identified and the templates found in thedatabase of known fingerprints do not match exactly. In that case, athresholding operation is carried out, to determine whether the twotemplates being matched are sufficiently similar. As indicated above,inexact matches may occur as a result of dirt or injuries to the fingersfrom which the fingerprints are taken, from rotation or distortion ofthe fingerprint image, or simply from poor quality fingerprints. Acorrelation coefficient is thus specified in the correlation between thetemplates being compared. If the correlation is above the correlationcoefficient the templates are considered a match, otherwise a match isnot reported. The value of the correlation coefficient may be varieddepending on the application of the system. If the correlationcoefficient is low, a greater incidence of false acceptance occurs,where an impostor is authenticated. A high correlation coefficientresults in a greater incidence of false rejection, where an authorizedindividual is rejected. The required correlation coefficient thus may beadjusted to suit the specific application of the system.

The methods of verification and identification according to embodimentsof the present invention provide for rapid comparison of fingerprints byusing templates generated from minutiae of an input fingerprint image.The speed of comparison is important particularly in identificationproblems, because databases of known fingerprints may be very large. Forexample, law enforcement fingerprint databases may contain tens ofmillions of entries, and rapid identification of fingerprints may bevital. In the case of identity verification, speed is also important,since the individual whose identity is being verified may need rapidaccess to data or to a location.

Embodiments of the system according to the present invention are alsocapable of performing identification and verification tasks when theinput fingerprint image is rotated relative to the reference fingerprinttemplates, or when the input image involves a partial fingerprint. Sincethe position of the minutiae generated by the system is defined inrelation to other minutiae in the template, not to an externalcoordinate system, rotating the input image does not affect the accuracyof the template matching system. If the input fingerprint image is apartial image, a probabilistic approach may be used to obtain a match ofthe templates. For example, for different size templates, individualrows of the first template may be compared to every row of the secondtemplate until a match is found. If no match is found, every row of thesecond template may be compare to all the rows of the first one, againlooking for a match.

FIG. 5 describes the steps that may be taken, according to an embodimentof the present invention, to generate a template and to perform anidentification or validation of the template. The process begins in step60, where the input fingerprint image is provided to the system. If theimage is not machine readable, it may be scanned, for example, andstored in a file readable by an electronic processor. The inputfingerprint image is smoothed in step 62, to remove noise from the inputfingerprint image. After the initial smoothing, the image is binarizedin step 64, as described above, to assign to each pixel of the image apixel value of 0 or 1. For example, the value 1 may be assigned topixels representing points on the fingerprint's crest lines, and thevalue 0 to all other pixels. In step 66 the binarized image is thinned,to normalize the width of all lines to one pixel.

A recursion loop starts in step 68, to analyze each pixel having a pixelvalue of 1. In step 70, a grid is formed around each of those pixels,extending one pixel away in all directions. This results in a grid with8 cells around the center cell. Moving along each of these cells, achange in pixel value from 0 to 1 is noted, and every time such changeoccurs, a transition sum value is increased by one. After all cells havebeen checked, the transition sum value is noted in step 72, and if it isat least equal to a selected value, the pixel in the center cell ismarked as a minutia. The minutiae are thus logged in step 72 for futureprocessing.

Once all the pixels representing minutiae are known, a template may begenerated in step 74 to record the minutiae and their location relativeto other minutiae. For example, the template may consist of databaseentries correlating each minutia, its distance vector from each of theother minutiae, and gradient information relative to the minutiae. Thetemplate may be stored in step 76 as a database in an electronic storagemedia which may be used by an electronic processor.

In step 78 a decision is made whether the newly generated template is tobe used in a verification or an identification step. In a verificationstep 82, the template is compared to a selected stored template derivedfrom known fingerprints, to validate the identity of the person fromwhom the template was generated. In identification step 80 the templateis compared to all templates stored in the database, to determine theidentity of the unknown individual from whom the input fingerprints wereobtained.

The present invention has been described with reference to specificembodiments. However, other embodiments may be devised that do notdepart from the scope of the invention. Accordingly, variousmodifications and changes may be made to the embodiments withoutdeparting from the broadest spirit and scope of the present invention asset forth in the claims that follow. The specification and drawings areaccordingly to be regarded in an illustrative rather than restrictivesense.

1. A method for fingerprint recognition, comprising the steps of:providing a machine readable input fingerprint image; smoothing theinput fingerprint image to remove noise; binarizing the smoothed inputfingerprint image to form a binary image; processing the binary image toidentify minutiae of the fingerprint image; superimposing a mask overportions of the binary image; averaging a first coordinate of pixelsdescribing the image features along line segments within the mask, eachof the line segments having a constant second coordinate; forming asequence of averaged first coordinate values for the line segments;identifying minutiae from the sequence of averaged first coordinatevalues; and generating a template describing the minutiae.
 2. The methodaccording to claim 1, further comprising the steps of: thinning thebinary image to normalize to one pixel a width of image features;recursively analyzing pixels describing the image features to determinea transition sum value of neighboring pixels; and identifying minutiaeat pixels where the transition sum value is at least equal to a selectedvalue.
 3. The method according to claim 2, further comprising the stepof: computing the transition sum value of each pixel by adding instancesof a change in pixel values of eight neighboring pixels surrounding thepixel.
 4. The method according to claim 2, the thinning step furtherincludes the substep of: normalizing the width of the image features ofthe binary image by drawing a one pixel wide line along a centerline ofthe image features.
 5. The method according to claim 1, the linesegments are parallel line segments.
 6. The method according to claim 1,further comprising the step of: assigning a pixel value of one to pixelsrepresenting a ridge, and a value of zero to pixels representing afurrow of the binary image.
 7. The method according to claim 6, furthercomprising the step of: defining a threshold value to distinguishbetween pixels representing a ridge and pixels representing a furrow. 8.The method according to claim 1, generating the template furtherincludes the substeps of: determining, for each of the minutiae,position information, and storing the position information in adatabase.
 9. The method according to claim 8, the position informationis a distance relative to the minutiae.
 10. The method according toclaim 1, further comprising the steps of: verifying the inputfingerprint image by comparing the generated template to a selectedstored template; and determining if the template and the selected storedtemplate are substantially the same.
 11. The method according to claim10, further comprising the step of: computing a correlation coefficientbetween the template and the selected stored template.
 12. The methodaccording to claim 1, further comprising the steps of: identifying theinput fingerprint image by comparing the generated template to storedtemplates of a database; and reporting those of the stored templatesmatching the generated template.
 13. A system for analyzingfingerprints, comprising: a software module configured to receive aninput fingerprint image, the input fingerprint image having firstportions representing fingerprint ridges and second portionsrepresenting fingerprint furrows, the first portions contain one of darkand light pixels, and the second portions contain another of dark andlight pixels, the software module being further configured to generate abinary image from the input fingerprint image, extract a set of minutiaefrom the binary image, superimpose a mask over segments of the binaryimage, average a first coordinate of dark pixels along line segmentswithin the mask, the first coordinate changing in value and each of theline segments having a second coordinate that is unchanging, generate asequence of averaged first coordinate values for the line segments, anddetect the presence of minutiae from the sequence of averaged firstcoordinate values; and a memory module configured to store a template oflocation information of the set of minutiae.
 14. The system according toclaim 13, further comprising: a further software module configured tocompare the template to a reference template.
 15. The system accordingto claim 14, the reference template is recursively selected fromtemplates in a database.
 16. The system according to claim 13, thebinary image is generated by assigning a pixel value of one to darkpixels of the input fingerprint image, and a value of zero to lightpixels of the input fingerprint image.
 17. The system according to claim16, a threshold darkness is specified to distinguish light and darkpixels.
 18. The system according to claim 16, for each pixel with pixelvalue of one, a transition sum value derived from changes in neighboringpixel values is computed.
 19. The system according to claim 18, eachpixel having a transition sum value derived from neighboring pixelvalues equaling selected values defines a minutia.
 20. The systemaccording to claim 13, the software module is configured to furthersmooth the input fingerprint image by deleting pixels not falling withinspecified parameters.
 21. The system according to claim 13, the binaryimage is thinned by normalizing a width of image features to a one pixelwidth.
 22. The system according to claim 13, a template of the minutiaeis formed at least from position information of the minutiae computedfrom the input fingerprint image.
 23. The system according to claim 22,the position information includes distance information between each oneof the minutiae and each other of the minutiae.
 24. The system accordingto claim 13, the first coordinate and the second coordinate areorthogonal.
 25. The system according to claim 13, the line segments areparallel line segments.
 26. The system according to claim 13 theminutiae are identified when, for a given second coordinate, a pointhaving a corresponding averaged first coordinate is not a dark pixel.